Are you sure that this is really why your site is heavy? I ask why I consider Bootstrap very light.
As for your question: Yes , it is perfectly possible.
This is provided by some frameworks. In the specific case of Bootstrap go to link and select only what you intend to use. There are other customizations possible as well.
I've heard of people deleting unused functions from the jQuery source code, however I do not recommend it as this might break some plugin. In this case there is no automated tool, you would have to do it yourself.
But I recommend you not to worry too much about it, as I find it very unlikely that Bootstrap / jQuery will be the performance bottleneck of your site. The most common mistake is to abuse Javascript.
Instead look for tips like the following: